7.40 Counts of picks in a one-pound bag. A guitar supply company must maintain s

Question

7.40 Counts of picks in a one-pound bag. A guitar supply company must maintain strict oversight on the number of picks they package for sale to customers. Their current advertisement specifies between 900 and 1000 picks in every bag. An SRS of 36 one-pound bags of picks was collected as part of a quality improvement effort within the company. The number of picks in each bag is shown in the following table. PICKS 924 925 967 909 959937 970 936 952 919 965 921 913 886 956 962 916 945 957 912 961 950 923 935 969 916 952 917 977 940 924 957 920 986 895 923 (a) Create (i) a histogram or a stemplot, (ii) a boxplot, and (ii) a Normal quantile plot of these counts. Write a care ful description of the distribution. Make sure to note any outliers, and comment on the skewness and Normality of the data. (b) Based on your observations in part (a), is it appropri- ate to analyze these data using the t procedures? Briefly explain your response. (c) Find the mean, the standard deviation, and the standard error of the mean for this sample. (d) Calculate the 90% confidence interval for the mean number of picks in a one-pound bag 7.41 Significance test for the average number of picks. Refer to the previous exercise.

Explanation / Answer

B) As the sample size n < 40 it is not very large we can use t procedure.

C) mean = 938.22

Standard deviation = 24.29

Standard error = 24.29/sqrt(36) = 4.048

D) DF = 36 - 1 = 35

With 35 degrees of freedom and 90% confidence interval the critical value is 1.69

The confidence interval is

Mean +/- t* * SE

= 938.22 +/- 1.69 * 4.048

= 938.22 +/- 6.84

= 931.38, 945.06

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